| Summary: | A generic tool for analyzing sparse approximation algorithms is the restricted isometry property (RIP) introduced by Candès and Tao (2005) [11]. If <i>R(k, n, N)</i> is the RIP constant with support size <i>k</i> for an <i>n × N</i> measurement matrix, we investigate the trend of reducing the support size of the RIP constants for qualitative comparisons between sufficient conditions. For example, which condition is easier to satisfy, <i>R</i>(4<i>k, n, N</i>) < 0.1 or <i>R</i>(<i>2k, n, N</i>) < 0.025? Using a quantitative comparison via phase transitions for Gaussian measurement matrices, three examples from the literature of such support size reduction are considered. In each case, utilizing a larger support size for the RIP constants results in a sufficient condition for exact sparse recovery that is satisfied by a significantly larger subset of Gaussian matrices.
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